A conventional cooling system of this type includes two cooling water channels and a valve for adjusting cooling water flow rates through these two cooling water channels. Through one of the cooling water channels, cooling water flows sequentially by way of a heat exchanger for air heating and a heat exchanger for transmission oil. The other one of the cooling water channels, which is provided separately from the above cooling water channel, includes a bypass passage. The valve is disposed at a point where the cooling water having passed the oil heat exchanger meets the cooling water having passed through the bypass passage. Such a conventional cooling system measures at least either of the vehicle interior temperature and the vehicle exterior temperature as well as the temperature of cooling water discharged from the engine, and controls the actuation of the valve so as to switch between these two cooling water channels when these temperature measurements satisfy their respective predetermined conditions (see Patent Document 1, for example).